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The order of the list assumes that you are starting from one of the faction shrines at Vale of Eternal Blossoms. The path is roughly circular. Some critters are listed more than once! This is due to spawn locations that are in different zones.

Valley of the Four WindsSifang Otter - check the river that flows south to Halfhill as you fly to Halfhill.Marsh Fiddler - try Halfhill first (you're probably going to need to travel there for your farm anyway) then in The Heartland.Bandicoon - check the area west of The Heartland as you fly through to Townlong Steppes.

Dread Wastes(Clouded Hedgehog - check the north edge of the zone, then fly around Zan'Vess if you didn't find it in Townlong Steppes.)Emperor Crab - the water between Zan'vess and Sogo's Gamble appears to have most dense spawn points.Amethyst Spiderling - generally spread out through the zone, try flying around Crane Wing Refuge first, maybe.Resilient Roach - check between Kypari Zar and Lake of Stars.

Krasarang WildsLuyu Moth - path from The Incursion to Zhu's Watch seems most dense.Malayan Quillrat - try Zhu's Watch.(Sifang Otter - check the coastline directly east of Zhu's Watch if you didn't find it in Valley of the Four Winds.)

The Jade ForestCoral Adder - north of Moonwater Retreat, approximately 67,80.Leopard Tree Frog - vicinity of Serpent's Heart.Shrine Fly - check land across bridge from Serpent's Heart (heading west).(Sifang Otter - check the water west of Paw'don Village if you didn't find it in either of the two previous places.)

The Veiled Stair(Bandicoon - If you didn't find bandicoon while flying through Valley of the Four Winds to Townlong Steppes, you can definitely find it here.)(Malayan Quillrat - If you didn't find it near Zhu's Watch in Krasarang Wilds, then try looking here.)